Robin条件下奇摄动单边界层问题的初值方法

Initial-Value Method for Singularly Perturbed Single Boundary Layer Problems with Robin Condition

研究初值方法在处理奇摄动Robin单边界层问题中的应用.该方法建立在奇摄动边界层理论基础上,可以用于解决具有单侧边界层现象的奇摄动两点边值问题.首先将给定的奇摄动两点边值问题转化为三个一阶初值问题,再将所得到的三个初值问题分别求解,最后得到原问题的近似,通过算例验证了该方法所得到的近似解能与精确解、数值解达到较好的一致.

The application of initial-value method in dealing with singularly perturbed Robin single boundary layer problem was studied.Based on the singularly perturbed boundary layer theory,this method can be used to solve singularly perturbed two-point boundary value problems with unilateral boundary layer phenomena.The basic process of this method is:firstly,the singularly perturbed two-point boundary value problem was transformed into three first-order initial value problems;then the three initial value problems are solved separately.Finally,the approximate solution of the original problem was obtained.Numerical examples shows that the approximate solution obtained by this method was in good agreement with the exact solution and numerical solution.